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</head>

<body lang=EN-CA style='tab-interval:.5in'>

<div class=WordSection1>

<h3>Battle Simulator</h3>

<p class=MsoNormal style='line-height:115%'>Our project seeks to migrate
tactical decisions from the realm of human scripting to the realm of AI. To
achieve this we have created a battle simulator to allow the computer to
anticipate the result of a battle. If it is possible to simulate the outcome of
battles, then it is possible to pick better strategies in battle. The hope is
that a simulator like this one could be used by an AI to make strategic
decisions instead of scripting specific instructions. </p>

<h5>Primary Goal</h5>

<p class=MsoNormal style='line-height:115%'>The goal of this project is to
simulate battles in StarCraft between two armies. Note that this goal is not to
have our army perform better, just to find the outcome of the battle. </p>

<h5>Secondary Goal</h5>

<p class=MsoNormal style='line-height:115%'>The secondary goal is to use the
battle simulator to evaluate a set of strategies and pick the most effective
one against an anticipated opponenets strategy( in this case, the computer
strategy). </p>

<h3>Assumptions</h3>

<ul type=disc>
 <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
     line-height:115%;mso-list:l0 level1 lfo1;tab-stops:list .5in'>The result
     of combat in a two dimensional world can be estimated in a one dimensional
     world we have created the following mechanics to simulate 2D combat
     situations </li>
 <ul type=circle>
  <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
      auto;line-height:115%;mso-list:l0 level2 lfo1;tab-stops:list 1.0in'>Range
      between units is kept track of. </li>
  <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
      auto;line-height:115%;mso-list:l0 level2 lfo1;tab-stops:list 1.0in'>A
      penalty on attack rate is imposed whenever a melee unit switches targets
      (time between attacks) </li>
  <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
      auto;line-height:115%;mso-list:l0 level2 lfo1;tab-stops:list 1.0in'>Blocking,
      units attempting to attack units behind enemy lines incur a penalty to
      speed while closing range. </li>
 </ul>
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     line-height:115%;mso-list:l0 level1 lfo1;tab-stops:list .5in'>Units of the
     same type will all want to attack the same target type </li>
 <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
     line-height:115%;mso-list:l0 level1 lfo1;tab-stops:list .5in'>There is no
     differentiation between target units of the same type </li>
 <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
     line-height:115%;mso-list:l0 level1 lfo1;tab-stops:list .5in'>Units will
     pursue and destroy their targets, and have no alternative motivations(i.e.
     no micro). </li>
</ul>

<h3>Modules</h3>

<h5>Strategy</h5>

<p class=MsoNormal style='line-height:115%'><span style='mso-no-proof:yes'><img
width=393 height=42 id="_x0000_i1027" src=Strategy.jpeg></span></p>

<h5>BattleSimulator</h5>

<p class=MsoNormal style='line-height:115%'><span style='mso-no-proof:yes'><img
width=260 height=177 id="_x0000_i1026" src=BattleSimulator.jpeg></span></p>

<h5>StrategyChooser</h5>

<p class=MsoNormal style='line-height:115%'><span style='mso-no-proof:yes'><img
width=281 height=170 id="_x0000_i1025" src=StrategyChooser.png></span></p>

<h3>Experiments</h3>

<h4>BattleSimulator</h4>

<p>These are experiments done on the battle simulator. In each case the
simulators initial prediction outcome is noted and then the combat is run 10
times in the real starcraft world. The outcome of the battle is noted in terms
of which units are left standing.</p>

<p>The experiments all assumed that the user would use the &quot;Alphabetical
Strategy&quot;, which attacks the units with the lowest alphanumeric value
first. Since we had control of these units, they behaved correctly. </p>

<p>The predicted strategy of the computer player is the CompStrat, which
attacks the units that have the lowest range(mostly the closest units). We
realized after testing that this is not the attack strategy the computer uses,
and thus our simulations lost quite a bit of accuracy. The computers strategy
is actually a great deal more complicated, with groups of units shifting focus
multiple times throughout the battle. </p>

<h5>8 Terran Marines vs. 9 Zerg Zerglings</h5>

<p class=MsoNormal style='line-height:115%'>This simulation was a straight
fight, with strategies irrelavant since there is only one possible target type.
The results show the simulator is very accurate in determining the result of a
battle without haveing to deal with strategies. </p>

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 mso-yfti-tbllook:1184'>
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  <td style='padding:.75pt .75pt .75pt .75pt'></td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>Marines</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>Zerglings</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:1'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>Predicted</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>4 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0 </p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:2'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 1 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>1 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0 </p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:3'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 2 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>2 </p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:4'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 3 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>4 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0 </p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:5'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 4 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>6 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0 </p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:6'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 5 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>4 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0 </p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:7'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 6 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>6 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0 </p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:8'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 7 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>5 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0 </p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:9'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 8 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>2 </p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:10'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 9 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0 </p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:11'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 10 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>1 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0 </p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:12'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>mean </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3.3 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0.4</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:13'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>median </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>4 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0 </p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:14;mso-yfti-lastrow:yes'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>mode </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>4 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0 </p>
  </td>
 </tr>
</table>

<h5>3 Terran Battlecruisers, 3 Terran Goliaths, 3 Terran Wraiths vs. self</h5>

<p class=MsoNormal style='line-height:115%'>This simulation is very interesting
since there are many possible targeting orders with significant differences.
With this simulation the battle simulator was able to conclusively identify the
strategy as poor, since attacking the battlecruisers leaves your opponents
firepower very high. <br>
P = player<br>
E = computer </p>

<table class=MsoNormalTable border=0 cellpadding=0 style='mso-cellspacing:1.5pt;
 mso-yfti-tbllook:1184'>
 <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
  <td style='padding:.75pt .75pt .75pt .75pt'></td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>PBC</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>PG</p>
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  <td style='padding:.75pt .75pt .75pt .75pt'>
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  <td style='padding:.75pt .75pt .75pt .75pt'>
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  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>EG</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>EW</p>
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 </tr>
 <tr style='mso-yfti-irow:1'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>Predicted</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
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  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>1</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:2'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 1 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>1</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:3'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 2 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>1</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:4'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 3 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>1</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:5'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 4 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:6'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 5 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:7'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 6 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>1</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:8'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 7 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>2</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:9'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 8 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>1</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:10'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 9 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>1</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:11'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 10 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>1</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:12'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>mean </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0.7</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>2.9</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:13'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>median </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>1</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:14;mso-yfti-lastrow:yes'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>mode </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>1</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
</table>

<h5>4 Protoss Zealots, 4 Protoss Dragoons vs. self</h5>

<p class=MsoNormal style='line-height:115%'>This simulation revealed
significant weaknesses in our simulator. Since the alphabetical strategy
demanded that the zealots attacked the dragoons, the zealots had to pass
through the enemy zealots and take considerably more time than the simulation
anticipated. This, combined with the computers cryptic targeting strategy, made
the predictions not ata all accurate. </p>

<table class=MsoNormalTable border=0 cellpadding=0 style='mso-cellspacing:1.5pt;
 mso-yfti-tbllook:1184'>
 <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
  <td style='padding:.75pt .75pt .75pt .75pt'></td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>PD</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>PZ</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>ED</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>EZ</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:1'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>Predicted</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:2'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 1 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>2</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:3'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 2 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:4'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 3 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:5'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 4 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:6'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 5 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:7'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 6 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>1</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:8'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 7 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:9'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 8 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>4</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:10'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 9 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>1</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:11'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>trail 10 </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:12'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>mean </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>2.6</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:13'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>median </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:14;mso-yfti-lastrow:yes'>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>mode </p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>0</p>
  </td>
  <td style='padding:.75pt .75pt .75pt .75pt'>
  <p class=MsoNormal style='margin-bottom:10.0pt;line-height:115%'>3</p>
  </td>
 </tr>
</table>

<h4>StrategyChooser</h4>

<h5>StratGen </h5>

<p>StratGen takes a inital ordering of possible strategy an then iterates
through a sub set of possible strategies and returns a strategy with said possibility.
StratChooser then takes each Strategy and runs it against our default computer
strategy. And then takes the resulting data and creates a Result object. It
compares that against the current best result object and if according to the
comparison is better than the new strategy is saved as the current best strategy.
This is done until all generated Strategies are done and this strategy is
implemented in the game. Result can be extended such that different types of comparisons
can be done. We just look at hit points. </p>

<p>To calculate the optimal strategy over all possible strategies is very
expensive and cannot be done in one frame.<span style='mso-spacerun:yes'>&nbsp;
</span>StratChooser and Battle Simulation can used to only run a portion of the
strategy</p>

<p>Per-Frame but this means the optimal strategy is not found until the battle
is under way.<span style='mso-spacerun:yes'>&nbsp; </span>For bigger battles it
may take a few seconds depending on how much calculating you want to do per
frame.</p>

<h3><o:p>&nbsp;</o:p></h3>

<h3>For the Future</h3>

<h5>Optimistic</h5>

<ul type=disc>
 <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
     line-height:115%;mso-list:l2 level1 lfo2;tab-stops:list .5in'>Able to
     accurately predict the result of some simple battles. </li>
 <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
     line-height:115%;mso-list:l2 level1 lfo2;tab-stops:list .5in'>Reasoning using
     the simulator is unlikely to generate bad strategies, since obviously
     terrible attack plans will not generate good results. The strategies may
     be sub-optimal though. </li>
 <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
     line-height:115%;mso-list:l2 level1 lfo2;tab-stops:list .5in'>With enough
     time, it could be adapted to be used on the fly with an AI to evaluate battle
     possibilities. </li>
</ul>

<h5>Pesimestic</h5>

<ul type=disc>
 <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
     line-height:115%;mso-list:l1 level1 lfo3;tab-stops:list .5in'>Programing
     the mechanics of the StarCraft in a 1-dimensional environment leaves out
     much of the game, and may leave out more than it includes. But without
     this abstraction, the simulator must deal with each unit seperately, increasing
     the n to a unmanagable level. </li>
 <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
     line-height:115%;mso-list:l1 level1 lfo3;tab-stops:list .5in'>Abstracting
     2D game effects takes a long time and may not give much payback to the
     actual accuracy of the simulator. </li>
</ul>

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